N. P. Lazarev, “Fictitious domain method in the equilibrium problem for a Timoshenko-type plate contacting with a rigid obstacle”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2013, Volume 13, Issue 1,Pages <nobr>91

This article is cited in 15 papers

Fictitious domain method in the equilibrium problem for a Timoshenko-type plate contacting with a rigid obstacle

N. P. Lazarev^ab

^a Lavrent'ev Institute of Hydrodynamics, Novosibirsk, Russia
^b Research Institute of Mathematics of North-Eastern Federal University, Yakutsk, Russia

Abstract: In this paper we study the nonlinear equilibrium problem for the plate with the Signorini condition on the part of the boundary. We construct a family of auxiliary problems defined in an extended domain so that their solutions converge properly to a solution of the Signorini problem. Each problem of this family describes the equilibrium of the plate with a crack. On the curve defining the crack we impose a boundary condition of an inequality type describing the non-penetration of opposite crack edges. Equivalent differential formulation of the problems is found.

Keywords: Signorini boundary conditions, fictitious domain, mutual non-penetration condition, Timoshenko-type plate, crack.

UDC: 539.311

Received: 04.04.2012